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Table 5 Calculated transformation parameters by ADQA, MPA, and OMA

From: Analytical dual quaternion algorithm of the weighted three-dimensional coordinate transformation

Rotation matrix

   

\({\mathbf{R}}\)

1.0000000000

0.0000047797

 − 0.0000043444

 

 − 0.0000047797

1.0000000000

 − 0.0000048370

 

0.0000043443

0.0000048371

1.0000000000

Rotation angles (″)

   

 θx

 

 − 0.997716

 

 θy

 

0.896085

 

 θz

 

0.985885

 

Translation (m)

   

 tx

 

641.8395

 

 ty

 

68.4729

 

 tz

 

416.2156

 

Scale

   

λ

 

1.000005611

 

Standard deviation of unit weight (m)

   

σ

 

0.1140

Â